DISSIPATIVE SCATTERING THEORY: AN OVERVIEW OF RECENT RESULTS (Mathematical aspects of quantum fields and related topics)

Abstract

We provide an introduction to the scattering theory of dissipative quantum systems representing the long-time evolution of a system interacting with another system S' and susceptible of being absorbed by S'. The effective dynamics of S is generated by an operator of the form H = H0 + V − iC∗on the Hilbert space of the pure states of S, where H0 is the self-adjoint generator of the free dynamics of S, V is symmetric and C is bounded. We define the basic objects of the scattering theory for the pair (H0), next we review recent results on the spectral singularities and the asymptotic completeness of the wave operators.